Explanation Given: The given conditions are f ( x ) = sin x and g ( x ) = cos x . Calculation: The D’ Alembert solution is, u ( x , t ) = 1 2 [ f ( x + a t ) + f ( x − a t ) ] + 1 2 a ∫ x − a t x + a t g ( s ) d s (1) The given condition is, f ( x ) = sin x (2) Substitute x = x + a t in the equation (2), f ( x + a t ) = sin ( x + a t ) Substitute x = x − a t in the equation (2), f ( x − a t ) = sin ( x − a t ) The second given condition is, g ( x ) = cos x Substitute x = s in the above equation, g ( s ) = cos s Substitute the values of f ( x + a t ) , f ( x − a t ) and g ( s ) in equation (1), u (<

Differential Equations with Boundary-Value Problems (MindTap Course List)

9th Edition

ISBN: 9781305965799

Author: Dennis G. Zill

Publisher: Cengage Learning

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Chapter 12.4, Problem 22E

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To solve: The initial value problem subjected to the given conditions.

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Chapter 12.4, Problem 21E

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The initial value problem subjected to the given conditions.

Solution Summary: The author explains the D' Alembert solution of the initial value problem subjected to the given conditions.

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